The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.
How many n-digit positive integers exist which are also an nth power?
def p63 c=0 i=1 m=1 while m<10 c+=(m..9).select{|j|(j**i).to_s.length==i}.length i+=1 m+=1 until ((m**i).to_s.length==i or m==10) end puts c end